Tensor Minkowski Functionals: first application to the CMB

Ganesan, Vidhya; Chingangbam, Pravabati

doi:10.1088/1475-7516/2017/06/023

Cited by 33 publications

(68 citation statements)

References 68 publications

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“…(See Table 2 of [34] for α values corresponding to different relative angles between two ellipses. )…”

Section: Review Of Tensor Minkowski Functionals On Flat 2-dimensionalmentioning

confidence: 99%

“…By visual inspection, we can see that both the diagonal elements of w 1 for all the fields are very different from Gaussian functions (compare with the expected functional form for Gaussian field given by Eq. (34) or Fig. (3)).…”

Section: Application To Galactic Foreground Fieldsmentioning

confidence: 99%

“…They can be classified into subsets of translation invariant and covariant tensors. In [34] Ganesan and Chingangbam introduced tensor-valued MFs for random fields defined on flat two-dimensional space and applied them to the CMB temperature and polarization fields. One of the translation invariant rank-2 MFs can capture the information about the shapes of individual hotspots and coldspots in the CMB fields (or any random field for that matter) and alignment in the spatial distribution of these structures.…”

Section: Introductionmentioning

confidence: 99%

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Tensor Minkowski Functionals for random fields on the sphere

Chingangbam

Yogendran

Joby

et al. 2017

J. Cosmol. Astropart. Phys.

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Abstract. We generalize the translation invariant tensor-valued Minkowski Functionals which are defined on two-dimensional flat space to the unit sphere. We apply them to level sets of random fields. The contours enclosing boundaries of level sets of random fields give a spatial distribution of random smooth closed curves. We outline a method to compute the tensor-valued Minkowski Functionals numerically for any random field on the sphere. Then we obtain analytic expressions for the ensemble expectation values of the matrix elements for isotropic Gaussian and Rayleigh fields. The results hold on flat as well as any curved space with affine connection. We elucidate the way in which the matrix elements encode information about the Gaussian nature and statistical isotropy (or departure from isotropy) of the field. Finally, we apply the method to maps of the Galactic foreground emissions from the 2015 PLANCK data and demonstrate their high level of statistical anisotropy and departure from Gaussianity.

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“…(See Table 2 of [34] for α values corresponding to different relative angles between two ellipses. )…”

Section: Review Of Tensor Minkowski Functionals On Flat 2-dimensionalmentioning

confidence: 99%

Section: Application To Galactic Foreground Fieldsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Tensor Minkowski Functionals for random fields on the sphere

Chingangbam

Yogendran

Joby

et al. 2017

J. Cosmol. Astropart. Phys.

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“…Applying higher ranked (tensor) Minkowski valuations to demixing DDFT calculations on spherical geometries in further studies may shed further light on the features of the universal properties of the demixing process. Tensor MF on the two-sphere  2 were introduced and applied in [44,45]. Higher ranked Minkowski tensor measures already proved to be useful in characterizing the solid-liquid phase transition in a twodimensional flat complex plasma [46].…”

Section: Discussionmentioning

confidence: 99%

Fluid demixing kinetics on spherical geometry: power spectrum and Minkowski functional analysis

et al. 2019

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Dynamic density functional theory calculations of fluid-fluid demixing on spherical geometries are characterized via their angular power spectrum as well as via the Minkowski functionals (MFs) of their binarized fluid density fields. MFs form a complete set of additive, motion invariant and continuous morphological measures sensitive to nonlinear (spatial) correlations. The temporal evolution of the fluid density fields is analyzed for different sphere sizes and mixing compositions. The demixing process in the stages of early spinodal decomposition and consecutive domain growth can be characterized by both methods and a power-law domain growth µ a ( ) L t t is evidenced for the MF measures. The average domain size obtained by the structure factor only responds to the late stage domain growth of the demixing process. MFs provide refined insights into the demixing process: they allow the detection of distinct stages in the early spinodal decomposition, provide a precise measure of the relative species composition of the mixture and, most importantly: after a proper rescaling, they allow the detection of a universal demixing behavior for a wide range of mixture fractions and for different sphere sizes.

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“…An alternative method of numerically reconstructing W 1 was adopted in [42] (see also [39]). In this section we briefly review the approach.…”

Section: Methods 2 -Using Identification Of Contours In Pixel Spacementioning

confidence: 99%

Morphology of CMB fields—effect of weak gravitational lensing

Goyal

Chingangbam

Appleby

2020

J. Cosmol. Astropart. Phys.

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We study the morphology of the cosmic microwave background temperature and polarization fields using the shape and alignment parameters, β and α, that are constructed from the contour Minkowski tensor. The primary goal of our paper is to understand the effect of weak gravitational lensing on the morphology of the CMB fields. In order to isolate different physical effects that can be potentially confused with the effect of lensing, we first study the effect of varying the cosmology on α and β, and show that they are relatively insensitive to variation of cosmological parameters. Next we analyze the signatures of hemispherical anisotropy, and show that information of such anisotropy in α gets washed out at small angular scales and become pronounced only at large angular scales. For β we find characteristic distortions which vary with the field threshold. We then study the effect of weak gravitational lensing using simulations of lensed temperature and E and B modes. We quantify the distortion induced in the fields across different angular scales. We find that lensing makes structures of all fields increasingly more anisotropic as we probe down to smaller scales. We find distinct behaviour of morphological distortions as a function of threshold for the different fields. The effect is small for temperature and E mode, while it is significantly large for B mode. Further, we find that lensing does not induce statistical anisotropy, as expected from the isotropic distribution of large scale structure of matter. We expect that the results obtained in this work will provide insights on the reconstruction of the lensing potential.

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Tensor Minkowski Functionals: first application to the CMB

Cited by 33 publications

References 68 publications

Tensor Minkowski Functionals for random fields on the sphere

Tensor Minkowski Functionals for random fields on the sphere

Fluid demixing kinetics on spherical geometry: power spectrum and Minkowski functional analysis

Morphology of CMB fields—effect of weak gravitational lensing

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